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Calculate the total amount collected on Thursday, excluding VAT, given attendance numbers and VAT-inclusive ticket prices.

Mathematics

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Answer

3.2

R312.51\text{R312.51}

Step-by-step solution

10 steps

Here are the solutions to the questions.

Part 3.1· 6 steps

  1. Determine the number of attendees for each ticket type on Thursday.

    • Total Adults = 53+57+40=15053 + 57 + 40 = 150
    • Total Students = 15+32+10=5715 + 32 + 10 = 57
    • Total Children = 9+15+9=339 + 15 + 9 = 33

  2. Identify the ticket prices for Thursday (inclusive of 10% VAT).

    From Table 5 (THURSDAY AND SUNDAY column):

    • Adult ticket price = 28.60 AUD
    • Student ticket price = 26.40 AUD
    • Children ticket price = 17.60 AUD

  3. Calculate the total amount collected for each ticket type, including VAT.

    • Total for Adults = 150×28.60 AUD=4290.00 AUD150 \times 28.60 \text{ AUD} = 4290.00 \text{ AUD}
    • Total for Students = 57×26.40 AUD=1504.80 AUD57 \times 26.40 \text{ AUD} = 1504.80 \text{ AUD}
    • Total for Children = 33×17.60 AUD=580.80 AUD33 \times 17.60 \text{ AUD} = 580.80 \text{ AUD}

  4. Calculate the total amount collected on Thursday, including VAT.

    Total collected (with VAT)=4290.00+1504.80+580.80=6375.60 AUD\text{Total collected (with VAT)} = 4290.00 + 1504.80 + 580.80 = 6375.60 \text{ AUD}

  5. Calculate the total amount collected excluding Australian VAT.

    Since the prices are inclusive of 10% VAT, the collected amount represents 110% of the amount excluding VAT.

    Amount excluding VAT=Total collected (with VAT)1+VAT rate\text{Amount excluding VAT} = \frac{\text{Total collected (with VAT)}}{1 + \text{VAT rate}} Amount excluding VAT=6375.60 AUD1.10=5796.00 AUD\text{Amount excluding VAT} = \frac{6375.60 \text{ AUD}}{1.10} = 5796.00 \text{ AUD}

  6. Verify the claim.

    The calculated amount collected, excluding Australian VAT, is 5796.00 AUD. The claim was that an amount of exactly 5796 AUD, excluding Australian VAT, was collected.
    Therefore, the claim is correct.

Part 3.2

R312.51\text{R312.51}

  1. Identify Keitumetse's ticket type and price for a Friday show.

    Keitumetse is a student, and she bought a ticket for a Friday show.
    From Table 5 (FRIDAY AND SATURDAY column):

    • Student ticket price = 30.50 AUD

  2. Convert the ticket price from Australian dollars (AUD) to United States dollars (USD).

    Given exchange rate: 1 AUD=0.71 USD1 \text{ AUD} = 0.71 \text{ USD}

    Cost in USD=30.50 AUD×0.71USDAUD=21.655 USD\text{Cost in USD} = 30.50 \text{ AUD} \times 0.71 \frac{\text{USD}}{\text{AUD}} = 21.655 \text{ USD}

  3. Convert the ticket price from United States dollars (USD) to South African rand (ZAR).

    Given exchange rate: 1 USD=14.43 ZAR1 \text{ USD} = 14.43 \text{ ZAR}

    Cost in ZAR=21.655 USD×14.43ZARUSD=312.50765 ZAR\text{Cost in ZAR} = 21.655 \text{ USD} \times 14.43 \frac{\text{ZAR}}{\text{USD}} = 312.50765 \text{ ZAR}

  4. Round the final answer to two decimal places for currency.

    Cost in ZAR≈312.51 ZAR\text{Cost in ZAR} \approx 312.51 \text{ ZAR}

    The ticket costs R312.51\boxed{\text{R312.51}} in South African rand.

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